Chapter 12.4, Problem 31HP

To determine

To explain: A real world situation where it is possible to change a cylinder to a cone and dimensions of cone if the volumes remain the same.

Answer to Problem 31HP

It is possible to change structure of torch light from cylinder to cone. Height of cone should be 3 times the height of cylinder.

Explanation of Solution

A torch light has a structure similar to cylinder. So it is possible to change the structure to a cone as it offer light up to a great range. Also it will be easy to handle.

Let the radius of the cone be r and height be h .

Let the radius of cylinder be $r\text{'}$ and height be $h\text{'}$ .

Volume of cone will be $\frac{1}{3}\pi r^{2}h$ and volume of cylinder will be $\pi {\left(r\text{'}\right)}^2\left(h\text{'}\right)$ .

Provided that the volumes should be same, so if the height of cone is increased to 3 times that of cylinder and radius should be same as that of cylinder then the volume won’t be affected.

Thus, it is possible to change structure of torch light from cylinder to cone. Height of cone should be 3 times the height of cylinder.